Name of the Department: Mathematics

Year of Establishment : 14^th June  1984

Programs  Offered : Mathematics at  FY & SY level for BSc and at FY level For BCOM

Pattern of Teaching Learning and Evaluation: 

Annual	Semester	Credit System
–	–	FYBSc/FYBCom/SYBSc

 

About the Department

 The college was established in the year 1984. Department of MATHEMATICS being started in the year 1984, since then Mathematics is taught at under graduate level for Commerce and Science streams. The Department aims to create a solid foundation for the assimilation of mathematical concepts and structures and build mathematical skills like creative, logical and analytical thinking. Software such as Maxima, GeoGebra, Mathematica etc. are used to increase the understanding of the fundamental mathematical concepts. The department has signed MOU with Zabuza Labs(Nashik), software development Company,  in the academic year 2019-20.The Department has been organizing activities like celebration of National Mathematics Day, Essay & Poster Competition that promotes student’s interests in the subject with their enthusiastic involvement.  Also Dept. has established Department Library in  academic year 2019-20.The department has received books of Rs.5261/- from “Madhava Mathematics Competition Cell ( Nashik District)”.

Vision of the  Department

 

• To develop the analytical and logical thinking of the students and their skills so that they can apply Mathematical methods to their real-life situations.

Mission Statement of the Department

 

• To develop the knowledge of our students and make them competent to face various competitive examinations
• To provide quality education to students in the subject so as to increase their employability.
• To popularize the subject among students.

Goals

 

• Remove the fear of Mathematics at an early stage and to create strong interest among the students in this vital subject .
• Encourage the students to participate actively in various activities like Avishhkar Research Project Competition, Departmental activities (poster and essay Competition, seminars ) etc.
• Encourage students to learn Mathematical concepts geometrically using various Mathematical Software namely Geogebra, Maxima, Scilab, Mathematica etc.
• To inculcate analytical, logical and critical thinking among the students.

B.Sc. (Honours/Honours with Research) (NEP)

 

• PROGRAM OUTCOMES(PO’s)-

• After successful completion of this program, students will be able to..

  1.enhance their logical thinking and apply advanced mathematical concepts to solve com- plex problems.

  2. formulate research questions, design experiments or investigations, collect and analyze data and present their findings in a clear and coherent manner.

  3. apply advanced mathematical techniques or tools to analyze and solve challenging problems encountered in mathematics and related fields.

  4. formulate mathematical models that represent real-world phenomena, analyze the models using mathematical methods and interpret the results to make informed decisions or predictions.

  5. develop proficiency in utilizing computational tools, software and programming languages to aid in mathematical analysis, numerical simulations and data visualization.

  6. present complex mathematical concepts, proofs and research findings to both technical and non-technical audiences.

  7. develop a strong foundation for professional growth and lifelong learning in Mathematics.

  8. acquire lifelong learning skills which will lead important to better opportunities and improve quality of life.

  9. gain knowledge with the holistic and multidisciplinary approach across the fields. 10. analyzing the results critically and applying acquired knowledge to solve the problems.

  11. be independent innovations and published it though research papers and projects.

  PROGRAM SPECIFIC OUTCOMES(PSO’s):

  The student will

  1. have a strong foundation for being research in mathematics.

  2. be able to apply mathematical skills for solving problems.

  3. at least basic knowledge of programming and computational techniques as required for employment.

  4. capable to analyze the results critically and apply acquired knowledge to solve the problems.

  5. have at least four different skills and capable to think and communicate in three different languages.

  6. be able prepare the models for real life problems

POs/COs/PSOs

Aims, Objectives and Outcomes of course [ Pattern 2019(Choice Based Credit System )]

Name of Course: B. Sc (Mathematics)

 I : Class:FYBSc

Aims: 

(i)Give the students a sufficient knowledge of fundamental principles, methods and a clear perception of innumerous power of mathematical ideas and tools and know how to use them by modeling, solving and interpreting.

(ii) Reflecting the broad nature of the subject and developing mathematical tools for continuing further study in various fields of science and technology.

(iii)Enhancing students’ overall development and to equip them with mathematical modeling abilities, problem solving skills, creative talent and power of communication necessary for various kinds of employment.

(iv) Enabling students to develop a positive attitude towards mathematics as an interesting and valuable subject of study.

Objectives: 

(i) A student should be able to recall basic facts about mathematics and should be able to display knowledge of conventions such as notations, terminology and recognize basic geometrical figures and graphical displays, state important facts resulting from their studies.

(ii) A student should get a relational understanding of mathematical concepts and concerned structures, and should be able to follow the patterns involved, mathematical reasoning.

(iii) A student should get adequate exposure to global and local concerns that explore them many aspects of Mathematical Sciences.

(iv) A student be able to apply their skills and knowledge, that is, translate information presented verbally into mathematical form, select and use appropriate mathematical formulae or techniques in order to process the information and draw the relevant conclusion.

(v) A student should be made aware of history of mathematics and hence of its past, present and future role as part of our culture.

Course Outcome:

Upon successful completion of this course, the student will be able to:

1. i) The mathematical maturity of students in their current and future courses shall develop.
2. ii) The student develops theoretical, applied and computational skills.

iii) The student gains confidence in proving theorems and solving problems.

Paper I: Algebra and Analytical Geometry

Expected Outcomes: 

1. Students will be understand the basic but important concepts of mathematics namely set, relations, functions, gcd, lcm etc.
2. Prove mathematical statements using mathematical Induction.

3. Solve various problems on properties of integers and use the basic concepts of divisibility, congruence and their applications in basic algebra.
4. Students will be understand the concept of complex number and related theory geometrically. Do the comparison between complex number and real number.
5. Solve the problems of lines in three dimensions, planes, spheres and how geometry is related to algebra by using their algebraic equations.

Paper II : Calculus

Expected Outcomes:

After completing the course, students will able to-

1. Identify algebraic and order properties of real numbers.
2. Identify and apply the function properties of real number system such as the completeness property
3. Verify the values of limit of a function at a point using the definition of a limit. Students develop knowledge in the limit, continuity and Students will be familiar with the techniques of differentiation of function with real variables.
4. Identify and apply the intermediate value theorem, Mean value theorem and L’Hospitals rule
5. Identify types of differential equations and solve differential equations such as Exact, homogeneous, non-homogeneous, and linear and Bernoulli differential equations etc.

Paper III: Practical

Expected Outcomes:

After completing the course, students will able to-

1.get the information about mathematical software’s free as well as paid.

2.learn how to handle maxima software and other mathematical software’s.

3.learn how to use mathematical software’s in learning process.

4.learn the mathematical concepts geometrically using maxima software.

5.use of Mathematical Software Maxima for better understanding of all mathematical concept.

6.verify the statement of theorems, lemmas and result using counter examples.

 

Name of Course: BCOM

Class : FYBCOM 

Semester: I

Business Mathematics & Statistics- I

Course Code – 114 (A) (No. of Credits :- 03) 

Objective of the Program:

1. To introduce the basic concepts in Finance and Business Mathematics and Statistics
2. To familiar the students with applications of Statistics and Mathematics in Business
3. To acquaint students with some basic concepts in Statistics.
4. To learn some elementary statistical methods for analysis of data.
5. The main outcome of this course is that the students are able to analyze the data by using some elementary statistical methods

Expected Outcomes:

After completing the course, students will able …

1. To understand the concept of Simple interest, compound interest, effect of compounding.
2. To understand the concept of Annuity and its applications for EMIs and Amortization Schedule.
3. To understand the concept of shares and mutual funds.
4. To understand contribution of shares and mutual funds in systematic investment plans
5. To solve problems related to shares and mutual funds.
6. To understand collection of data, analyzing and interpreting data.
7. To Know different method of sampling
8. To classify and represent data in tabular and graphical form.
9. To compute various measures of central tendency and measures of dispersion

Class : FYBCOM

Semester: II

Business Mathematics & Statistics- II

Course Code – 124 (B) (No. of Credits :- 03) 

Depth of the program – Basic Knowledge of Mathematics and Statistics

Objective :

1. To introduce the basic concepts in Finance and Business Mathematics and Statistics
2. To familiar the students with applications of Statistics and Mathematics in Business
3. To acquaint students with some basic concepts in Statistics.
4. To learn some elementary statistical methods for analysis of data.
5. The main outcome of this course is that the students are able to analyze the data by using some elementary statistical methods.

Expected Outcomes:

After completing the course, students will able …

1.To understand the concept of matrices and determinants.

2.To understand the application of determinant in solving linear equations

3.To understand applications of matrices and determinants in business and economics.

4.To understand the concept of LPP and its application in business and decision making.

5.To understand graphical method to solve business optimization problems with two variables.

6.To use correlation for knowing the relationship between two variables.

7.To use regression for prediction.

8.To know different types index numbers and problems in their construction.

9.To know the applications of various index numbers.

Name of Course: B. Sc (Mathematics)

Class : SYBSc 

 Aims:

• Give the students a sufficient knowledge of fundamental principles, methods and a clear perception of innumerous power of mathematical ideas and tools and know how to use them by modeling, solving and interpreting.
• Reflecting the broad nature of the subject and developing mathematical tools for continuing further study in various fields of science.
• Enhancing students’ overall development and to equip them with mathematical modeling abilities, problem solving skills, creative talent and power of communication necessary for various kinds of employment.
• Enabling students to develop a positive attitude towards mathematics as an interesting and valuable subject of study.

Objectives:

• A student should be able to recall basic facts about mathematics and should be able to display knowledge of conventions such as notations, terminology and recognize basic geometrical figures and graphical displays, state important facts resulting from their studies.
• A student should get a relational understanding of mathematical concepts and concerned structures, and should be able to follow the patterns involved, mathematical reasoning.
• A student should get adequate exposure to global and local concerns that explore them many aspects of Mathematical Sciences.
• A student be able to apply their skills and knowledge, that is, translate information presented verbally into mathematical form, select and use appropriate mathematical formulae or techniques in order to process the information and draw the relevant conclusion.
• A student should be made aware of history of mathematics and hence of its past, present and future role as part of our culture.

Outcomes of Course:

Upon completion of the course, the students will achieve the following.

(i) The mathematical maturity of students in their current and future courses shall develop.

(ii) The student develops theoretical, applied and computational skills.

(iii) The student gains confidence in proving theorems and solving problems.

Paper  I  :MT-231: Calculus of Several Variables( Sem. I)

Expected Outcomes : 

1.Students will be understand the function of several variables ( at least 2 or 3 variables) and basic notions related to it like graphs, level curve/surface, limit and continuity of functions geometrically.

2.Studentds will able to find higher order partial derivatives and apply chain rule.

3.Studends will be able to solve extreme values problems and apply to real life situations.

4.Students will be able to solve the examples of the double and triple integrals.

5.Students will able to apply the concepts of mathematics in real life situations. 

Paper II(A): Numerical Methods and it’s Applications (Sem. I) 

Expected Outcomes:

After completing the course, students will able to-

1. Identify algebraic , exponential and logarithmic Functions.
2. Identify Absolute ,relative and Percentage errors and general error formula.
3. To find the root of equations by various methods like Bisection method, False Position and Newton methods.
4. Develop knowledge in the interpolation by using forward, backward and Lagrange’s formula
5. To find first and second differentiation and integration by using Trapezoidal, Simpson’s Rules from given data and
6. To develops the techniques to find more correct approximations by Euler’s and Euler’s modified method of first order differential equations. Also by using Runge –Kutta Second and Forth order formula.

Paper  I  : MT-241: Linear Algebra ( Sem. II)

Expected Outcomes :

After completing the course, students will able to-

1.solve system of linear equation using row echelon and reduced row echelon form.

2.identify whether the given set is vector space or not.

3.check linear dependence and independence of the given set.

4.write basis and dimension of standard vector spaces.

5.find Row, Column and Null Space of a matrix.

6.identify whether given function is a linear Transformation or not

7.solve problems related Kernel and range of a linear Transformation, Rank-Nullity theorem Composite and Inverse Transformation.

8.find matrix of a Linear Transformation.

9.solve the examples of the Linear Isomorphism.

Paper III: Practical 

Expected Outcomes:

After completing the course, students will able to-

1.get the information about mathematical software’s free as well as paid.

2.learn how to handle maxima software and other mathematical software’s.

3.learn how to use mathematical software’s in learning process.

4.learn the mathematical concepts geometrically using maxima software.

5.use of Mathematical Software Maxima for better understanding of all mathematical concept.

6.verify the statement of theorems, lemmas and result using counter examples.